Re: ellgenerators

[Kevin Acres <research@research-systems.com>]

Hi Max,

I've recently extracted many 10's of millions of MW curves with 
conductors in the region of 10^32.  It's fairly easy to issue a 
system call to ratpoints from gp in order to get an list of rational 
points.  From there, it's just a few more lines of gp script to 
extract the generators and determine a lower bound for rank.  The 
whole process usually takes just a few milliseconds per curve.

Currently I'm processing about 300,000 curves per day in this fashion but
discarding anything less than rank 8.

If you want some code samples please let me know.


Best Regards,

Kevin.


At 08:35 PM 30/05/2012, Max Alekseyev wrote:
> Why pari cannot compute generators of an elliptic curve, while sage can?
> I thought they have roughly the same "power" w.r.t. elliptic curves.
>
> ? ellgenerators(ellinit([-35750837071872,63237970697887678464]))
>   ***   at top-level: ellgenerators(ellini
>   ***                 ^--------------------
>   *** ellgenerators: error opening elldata file:
> `/usr/local/share/pari/elldata/ell1816'.
>   ***   Break loop: type 'break' to go back to GP
>
> sage: EllipticCurve([-35750837071872,63237970697887678464]).gens()
> [(-2365632 : 11600547840 : 1)]
>
> Thanks,
> Max